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Symplectic maps for the n-body problem - Stability analysisThe stability of new symplectic n-body maps is examined from the point of view of nonlinear dynamics. The resonances responsible for the principal artifacts are identified. These are resonances between the stepsize and the difference of mean motions between pairs of planets. For larger stepsizes resonant perturbations are evident in the variation of the energy of the system corresponding to these stepsize resonances. It is shown that the principal instability of the method can be predicted and corresponds to the overlap of the stepsize resonances. It is noted that the analysis suggests that other artifacts will occur. For example, the overlap of a stepsize resonance with a resonance of the actual system may also give a region of chaotic behavior that is an artifact. It is pointed out that the fact that the principal artifacts corresponds to a particular set of stepsize resonances suggests that it may be possible to perturbatively remove the effect when the stepsize resonances are nonoverlapping.
Document ID
19930030760
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Wisdom, Jack
(NASA Headquarters Washington, DC United States)
Holman, Matthew
(MIT Cambridge, MA, United States)
Date Acquired
August 16, 2013
Publication Date
November 1, 1992
Publication Information
Publication: Astronomical Journal
Volume: 104
Issue: 5
ISSN: 0004-6256
Subject Category
Astrophysics
Accession Number
93A14757
Funding Number(s)
CONTRACT_GRANT: NSF AST-88-57365
CONTRACT_GRANT: NAGW-706
Distribution Limits
Public
Copyright
Other

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